Stochastic simulation can be applied to estimate the number of feasible solutions in a combinatorial problem. This idea will be illustrated to count the number of possible Sudoku grids. It will be argued why this becomes a rare-event simulation, and how an importance sampling algorithm resolves this difficulty.

It is shown that importance sampling can be effectively applied to the pricing of a single tranche of a CDO. In particular, by shifting the mean of the common factor, it is demonstrated that the price can be estimated to an accuracy of approximately one percent with about ten thousand paths in a large range of cases. This is achieved at minimal extra computational complexity.

Abstract Annealed Importance Sampling (AIS) is a popular algorithm used to estimates the intractable marginal likelihood of deep generative models. Although AIS guaranteed provide unbiased estimate for any set hyperparameters, common implementations rely on simple heuristics such as geometric average bridging distributions between initial and target distribution which affect estimation performa...